Dimension reduction of bivariate population balances using the quadrature method of moments

Crystallizationmodels with direction-dependent growth rates give rise tomulti-dimensional population balance equations (PBE) that require a high computational cost. We propose a model reduction based on the quadrature method of moments (QMOM). Using this method a two-dimensional population balance is reduced to a system of one-dimensional advection equations. Despite the dimension reduction the method keeps important volume dependent information of the crystal size distribution (CSD). It returns eywords: rystallization irection-dependent growth ulti-dimensional population balances uadrature method of moments the crystal volumedistribution aswell as other volumedependentmoments of the two-dimensional CSD. Themethod is applied to amodel problemwith direction-dependent growth of barium sulphate crystals, and shows good performance and convergence in these examples. We also compare it on numerical examples to another model reduction using a normal distribution ansatz approach. We can show that our method still gives satisfactory results where the other approach is not suitable. pwind-MUSCL scheme econd order finite volume scheme